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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 38640.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38640.s1 | 38640bp1 | \([0, -1, 0, -2576, 48576]\) | \(461710681489/27048000\) | \(110788608000\) | \([2]\) | \(41472\) | \(0.87269\) | \(\Gamma_0(N)\)-optimal |
38640.s2 | 38640bp2 | \([0, -1, 0, 1904, 195520]\) | \(186267240431/4165875000\) | \(-17063424000000\) | \([2]\) | \(82944\) | \(1.2193\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.s have rank \(1\).
Complex multiplication
The elliptic curves in class 38640.s do not have complex multiplication.Modular form 38640.2.a.s
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.